A biquaternionic version of the Dirac Equation is introduced, with a procedure for converting four-component spinors to elements of the Pauli algebra. In this version, mass appears as a coefficient between the 4-gradient of a spinor and its image under an outer automorphism of the Pauli algebra. The charge conjugation operator takes a particulary simple form in this formulation and switches the sign of the mass coefficient, so that for a solution invariant under charge conjugation the mass has to equal zero. The multiple of the charge conjugation operator by the imaginary unit turns out to be a complex Lorentz transformation. It commutes with the outer automorphism, while the charge conjugation operator itself anticommutes with it, providing a second more algebraic proof of the main theorem. Considering the Majorana equation, it is shown that non-zero mass of its solution is imaginary.

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双四元数狄拉克方程预测马约拉纳费米子的零质量

介绍了狄拉克方程的双四元数版本，以及将四分量旋量转换为泡利代数元素的过程。在这个版本中，质量表现为自旋量的 4 梯度与其在泡利代数的外自同构下的图像之间的系数。在这个公式中，电荷共轭算子采用了一种特别简单的形式，并转换了质量系数的符号，因此对于电荷共轭下不变量的解，质量必须为零。虚数单位的电荷共轭算子的倍数结果是一个复杂的洛伦兹变换。它与外部自同构交换，而电荷共轭算子本身与它反交换，提供了主定理的第二个代数证明。考虑马约拉纳方程，